Question: Solve for $x$ and $y$ using elimination. ${-3x+3y = 27}$ ${-2x-3y = -32}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. $-5x = -5$ $\dfrac{-5x}{{-5}} = \dfrac{-5}{{-5}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-3x+3y = 27}\thinspace$ to find $y$ ${-3}{(1)}{ + 3y = 27}$ $-3+3y = 27$ $-3{+3} + 3y = 27{+3}$ $3y = 30$ $\dfrac{3y}{{3}} = \dfrac{30}{{3}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {-2x-3y = -32}\thinspace$ and get the same answer for $y$ : ${-2}{(1)}{ - 3y = -32}$ ${y = 10}$